The non-Hermitian Hamiltonian of the dissipative AB chain illustrated in Fig. REF  is given by [1]}, [2]}
\(\begin{aligned}H=& \sum _{n=1}^{N}[J_pb^\dagger _na_n+J_sc^\dagger _nb_n+J_se^{i\phi }a^\dagger _nc_n+{H.c.}]\\&+\sum _{n=1}^{N-1} [J_ta^\dagger _{n+1}b_n+{H.c.}]+ \sum _{n=1}^{N}(\Delta -i\gamma )c_n^\dagger c_n.\end{aligned}\) 
